Ph.D. Candidate: John Dodaro
Research Advisor: Steven Kivelson
Date: Tuesday, June 4th 2019
Location: McCullough 335
Title: Generalization of Anderson's theorem for disordered superconductors
Abstract: The robustness of the critical temperature and energy gap of conventional superconductors to non-magnetic impurities can be understood through Anderson's "theorem" by pairing exact time-reversed states; however, the theorem is not applicable to a sign-changing order parameter as the dirty limit is not well-defined. Moreover, the perturbative and effective medium approximations typically employed to treat the suppression of superconductivity are only valid under certain assumptions about the disorder ensemble and coherence length. We show that at the level of BCS mean-field theory, the superconducting Tc is always increased in the presence of disorder, regardless of order parameter symmetry, disorder strength, and spatial dimension. This result reflects the physics of rare events -- formally analogous to the problem of Lifshitz tails in disordered semiconductors -- and arises from considerations of spatially inhomogeneous solutions of the gap equation. If the clean-limit superconducting coherence length ξ0 is large compared to disorder correlation length α, when fluctuations about mean-field theory are considered, the effects of such rare events are small -- typically exponentially (ξ0/α)d. When this ratio is of the order unity, these considerations are important. We present a generalization of Anderson's theorem for dirty superconductors and discuss possible relevance to the overdoped cuprates.